Correlation energy of two electrons in the high-density limit

Pierre-François Loos; Peter M W Gill

doi:10.1063/1.3275519

Correlation energy of two electrons in the high-density limit

J Chem Phys. 2009 Dec 28;131(24):241101. doi: 10.1063/1.3275519.

Authors

Pierre-François Loos¹, Peter M W Gill

Affiliation

¹ Research School of Chemistry, Australian National University, Canberra, Australian Capital Territory 0200, Australia. loos@rsc.anu.edu.au

PMID: 20059043
DOI: 10.1063/1.3275519

Abstract

We consider the high-density-limit correlation energy E(c) in D > or = 2 dimensions for the (1)S ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the E(c) values are strikingly similar, depending strongly on D but only weakly on the external potential. We conjecture that for large D, the limiting correlation energy E(c) approximately -delta(2)/8 in any confining external potential, where delta = 1/(D-1).